Conclusion

In this chapter, you have examined different ways to solve equations. You started out with the notion that an equation involves a relation of equality or balance. To solve an equation, you engage in a process of changing the equation in a way that sustains the balance but at the same time allows you to isolate a given variable so that you can determine its value. To solve equations, you use the properties of addition and multiplication. You use these properties to “undo” operations that the equation contains. In addition to working with addition and multiplication (which includes subtraction and division), you also dealt with the use of least common denominators to clear fractions from equations. You also worked with absolute values, which leave you with equations that have two solutions, and inequalities, which often leave you with extended sets with an indefinite number of elements.